常微分方程及其应用

Chapter 1 First．order Differential Equations

1．1 Introduction

Exercise 1．1

1．2 First—order Linear Differential Equations

1．2．1 First—order Homogeneous Linear Differential Equations

1．2．2 First—order Nonhomogeneous Linear Differential Equations

1．2．3 Bernoulli Equations

Exercise 1．2

1．3 Separable Equations

1．3．1 Separable Equations

1．3．2 Homogeneous Equations

Exercise 1．3

1．4 Applications

Module 1 The Spread of Technological Innovations

Module 2 The Van Meegeren Art Forgeries

1．5 Exact Equations

1．5．1 Criterion for Exactness

1．5．2 Integrating Factor

Exercise 1 5

1．6 Existence and Uniqueness of Solutions

Exercise 1．6

Chapter 2 Second．order Differential Equations

2．1 General Solutions of Homogeneous Second—order Linear Equations

Exercise 2．1

2．2 Homogeneous Second—order Linear Equations with Constant Coeffcients

2．2．1 The Characteristic Equation Has Distinct Real Roots

2．2．2 The Characteristic Equation Has Repeated Roots

2．2．3 The Characteristic Equation Has ComNeX Conjugate Roo~s

Exercise 2．2

2．3 Nonhomogeneous Second—order Linear Equations

2．3．1 Structure of General Solutions

2．3．2 Method of Variation of Parameters

2．3．3 Methods for Some Special Form of the Nonhomogeneous Term g(t)

Exercise 2．3

2．4 Applications

Module 1 An Atomic Waste Disposal Problem．

Module 2 Mechanical Vibrations

Chapter 3 Linear Systems of Differential Equations

3．1 Basic Concepts and Theorems

Exercise 3．1

3．2 The Eigenvalue-Eigenvector Method of Finding Solutions

3．2．1 The Characteristic Polynomial of A Has n Distinct Real

Eigenvalues

3．2．2 The Characteristic Polynomial of A Has Complex Eigenvalues

3．2．3 The Characteristic Polynomial of A Has Equal Eigenvalues

Exercise 3．2

3．3 YhndamentM Matrix Solution；Matrix—valued Exponential Function eAt

Exercise 3．3

3．4 Nonhomogeneous Equations；Variation of Parameters

Exercise 3．4

3．5 Applications

Module 1 The Principle of Competitive Exclusion in Population Biology．

Module 2 A Model for the Blood Glucose Regular System

Chapter 4 Laplace Transforms and Their Applications in Solving Differential Equations

4．1 Laplace Transforms

Exercise 4．1

4．2 Properties of Laplace Transforms

Exercise 4．2

4．3 Inverse Laplace Transforms

Exercise 4．3

4．4 Solving Differential Equations by Laplace Transforms

……

Chapter 5 Introduction to the Stability Theory

Answers to Selected Exercises

References

附录 软件包Iode简介

《常微分方程及其应用：理论与模型》是常微分方程课程的英文教材，是作者结合多年的双语教学经验编写而成。全书共5章，包括一阶线性微分方程，高阶线性微分方程，线性微分方程组。Laplace变换及其在微分方程求解中的应用，以及微分方程的稳定性理论。书中配有大量的应用实例和用Matlab软件绘制的微分方程解的相图，并介绍了绘制相图的程序。
本书可作为高等院校理工科偏理或非数学专业的本科双语教材，也可供相关专业的研究生、教师和广大科技人员参考。